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Calculus · Definite-Integrals

Integrate 2x from 0 to 1/2

\int_{0}^{\frac{1}{2}} 2 x\, dx

Step by step

  1. \int_{0}^{\frac{1}{2}} 2 x\, dx

    First find an antiderivative F, then evaluate F(b) − F(a).

  2. \int 2 x\, dx = 2 \int x\, dx

    Pull the constant 2 out of the integral.

  3. \int x\, dx = \frac{x^{2}}{2}

    Power rule: ∫xⁿ dx = xⁿ⁺¹/(n+1) (n ≠ −1).

  4. F(\frac{1}{2}) - F(0) = \left(\frac{1}{4}\right) - \left(0\right)

    Fundamental theorem of calculus: plug in the limits.

  5. = \frac{1}{4}

    Simplify.

Reveal the answer
\frac{1}{4}